This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linea...This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linearization or any restrictive assumption of any form in providing analytical or approximate solutions to linear and nonlinear equation without the integral related with nonlinear term. Theses virtues make it to be reliable and its efficiency is demonstrated with numerical examples.展开更多
An improved perturbation procedure is used for analyzing the radiation character-istics of the millimeter wave dielectric grating leaky wave antenna. The electromagnetic fields aredescribed in terms of an active trans...An improved perturbation procedure is used for analyzing the radiation character-istics of the millimeter wave dielectric grating leaky wave antenna. The electromagnetic fields aredescribed in terms of an active transverse transmission line network, which brings considerablephysical insight into the overall behavior of the antenna. The analysis is simple and practical. Itsaccuracy is as high as the rigorous method.展开更多
This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matr...This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.展开更多
Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of pertur...Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.展开更多
Recently,much attention has been focused on the false vacuum islands that are flooded by an expanding ocean of true-vacuum bubbles slightly later than most of the other parts of the world.These delayed decay regions w...Recently,much attention has been focused on the false vacuum islands that are flooded by an expanding ocean of true-vacuum bubbles slightly later than most of the other parts of the world.These delayed decay regions will accumulate locally larger vacuum energy density by staying in the false vacuum longer than those already transited into the true vacuum.A false vacuum island with thus acquired density contrast of a super-horizon size will evolve locally from radiation dominance to vacuum dominance,creating a local baby Universe that can be regarded effectively as a local closed Universe.If such density contrasts of super-horizon sizes can ever grow large enough to exceed the threshold of gravitational collapse,primordial black holes will form similar to those collapsing curvature perturbations on super-horizon scales induced by small-scale enhancements during inflation.If not,such density contrasts can still induce curvature perturbations potentially observable today.In this paper,we revisit and elaborate on the generations of primordial black holes and curvature perturbations from delayed-decayed false vacuum islands during asynchronous first-order phase transitions with fitting formulas convenient for future model-independent studies.展开更多
When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial e...When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.展开更多
文摘This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linearization or any restrictive assumption of any form in providing analytical or approximate solutions to linear and nonlinear equation without the integral related with nonlinear term. Theses virtues make it to be reliable and its efficiency is demonstrated with numerical examples.
文摘An improved perturbation procedure is used for analyzing the radiation character-istics of the millimeter wave dielectric grating leaky wave antenna. The electromagnetic fields aredescribed in terms of an active transverse transmission line network, which brings considerablephysical insight into the overall behavior of the antenna. The analysis is simple and practical. Itsaccuracy is as high as the rigorous method.
基金Project supported by the National Natural Science Foundation of China(No.10672194)the China-Russia Cooperative Project(the National Natural Science Foundation of China and the Russian Foundation for Basic Research)(No.10811120012)
文摘This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.
基金The project supported by National Natural Science Foundation of China under Grant No. 10375022 and the Scientific Research Fund of the Education Department of Hunan Province of China under Grant No. 05C414
文摘Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.
基金supported by the National Key Research and Development Program of China(Grant Nos.2021YFC2203004,2021YFA0718304,and 2020YFC2201502)the National Natural Science Foundation of China(Grant Nos.12105344,12235019,11821505,11991052,and 11947302)+3 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(CAS)(Grant Nos.XDB23030100,and XDA15020701)the Key Research Program of the CAS(Grant No.XDPB15)the Key Research Program of Frontier Sciences of CASthe Science Research Grants from the China Manned Space Project(Grant No.CMS-CSST-2021-B01)。
文摘Recently,much attention has been focused on the false vacuum islands that are flooded by an expanding ocean of true-vacuum bubbles slightly later than most of the other parts of the world.These delayed decay regions will accumulate locally larger vacuum energy density by staying in the false vacuum longer than those already transited into the true vacuum.A false vacuum island with thus acquired density contrast of a super-horizon size will evolve locally from radiation dominance to vacuum dominance,creating a local baby Universe that can be regarded effectively as a local closed Universe.If such density contrasts of super-horizon sizes can ever grow large enough to exceed the threshold of gravitational collapse,primordial black holes will form similar to those collapsing curvature perturbations on super-horizon scales induced by small-scale enhancements during inflation.If not,such density contrasts can still induce curvature perturbations potentially observable today.In this paper,we revisit and elaborate on the generations of primordial black holes and curvature perturbations from delayed-decayed false vacuum islands during asynchronous first-order phase transitions with fitting formulas convenient for future model-independent studies.
基金supported by the National Natural Science Foundation of China(61071187)Key Laboratory Foundation for Underwater Test and Control Technology(9140c260201110c26)
文摘When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.
